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\usepackage{amsmath}
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\begin{document}\definecolor{fgC}{rgb}{0,0,0}\color{fgC}\[\begin{matrix}
U_t = R(U)  \Leftrightarrow U_t = F(U)_x \\
U = \begin{bmatrix}
\rho_s \\
\rho u \\
\rho E
\end{bmatrix}\;\;\;
F(U) = \begin{bmatrix}
\rho_s u \\
\rho u^2 + p \\
\rho u H
\end{bmatrix}\;\;\; for\; s=1,2,...N_s \\
\rho = \sum_{s=1}^{N_s}\rho_s \\
c_p = \sum_{s=1}^{N_S} \frac{\rho_s}{\rho} c_{p,s} \quad  c_v = \sum_{s=1}^{N_S} \frac{\rho_s}{\rho} c_{v,s}
\end{matrix}  \]\end{document}